document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203977>Question 1203977</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Joseph invested a total of $10,000$10,000 in two accounts. After a year, one account lost 7.8%, while the other account gained 6.7%. In total, Joseph lost \$562.50. How much money did Joseph invest in each account?Write and solve a system of equations to answer the following questions.Joseph invested in the account with 7.8% loss.Joseph investedin the account with 6.7% gain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839950 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839950\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The overall percentage change was -562.50/10000 = -.05625 = -5.625%.<br><BR>\n" );
document.write( "Before doing any calculations, note that this percentage is much closer to -7.8% than it is to +6.7%, so by far the larger amount was invested in the account that lost 7.8%.<br><BR>\n" );
document.write( "A solution using the typical formal algebraic method...<br><BR>\n" );
document.write( "x = amount invested in account that gained 6.7%<BR>\n" );
document.write( "10000-x = amount invested in account that lost 7.8%<br><BR>\n" );
document.write( "The overall change was a loss of $562.50:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28.067%28x%29%29%2B%28.078%2810000-x%29%29=-562.5 ALIGN=MIDDLE  ALT=\"%28.067%28x%29%29%2B%28.078%2810000-x%29%29=-562.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.067x-780%2B.078x=-562.5 ALIGN=MIDDLE  ALT=\".067x-780%2B.078x=-562.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.145x=217.5 ALIGN=MIDDLE  ALT=\".145x=217.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=217.5%2F.145=1500 ALIGN=MIDDLE  ALT=\"x=217.5%2F.145=1500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: $1500 was invested in the account that gained 6.7%; the other $8500 in the account that lost 7.8%<br><BR>\n" );
document.write( "CHECK: .067(1500)-.078(8500) = 100.50-663 = -562.50<br><BR>\n" );
document.write( "You can also solve any 2-part \"mixture\" problem like this informally, performing virtually the same calculations but without the formal algebra.<br><BR>\n" );
document.write( "The three percentages in the problem are -7.8, -5.625, and +6.7.<br><BR>\n" );
document.write( "Look at those percentages on a number line and determine that -5.625 is (2.175)/(14.5) = .15 of the way from -7.8 to +6.7.<br><BR>\n" );
document.write( "That means .15 or 15% of the total was invested in the account that gained 6.7%.<br><BR>\n" );
document.write( "ANSWER: 15% of the $10,000, or $1500, was invested in the account that gained 6.7%; the other $8500 was invested in the account that lost 7.8%.<br><BR>\n" );
document.write( "Note that in this problem, since the numbers were \"ugly\", the informal method wasn't much easier than the formal algebraic method.  But with \"nice\" numbers that are easy to work with mentally, the informal method can get you to the solution with far less effort.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );